Garden
Grove
Unified
School
District
Precalculus
Q3
Benchmark
Review
09‐10
Scientific
Calculators
are
permitted
1. T 15.0 What are the polar coordinates of the
point with rectangular coordinates (5, 6) ?
(Round to tenths)
2. T 15.0 What are the rectangular coordinates
5p
of the point with polar coordinates (6, ) ?
6
3. T 15.0 Which of the following polar
coordinates does not describe (-2 2 ,-2 2) ?
Explain why.
5p
)
4
p
c) (-4, )
4
a) (4,
3p
)
4
p
d) (4,- )
4
b) (4,-
4. T16.0 What is the polar equation for the
circle with the equation x 2 + (y - 3) 2 = 9 ?
11. T18.0 What is the first step to find the three
third roots of i?
12. T 18.0 What are the cube roots of
8(cos135∞ + i sin135∞) ? Leave answers in
trigonometric (polar) form.
13. T 18.0 What are the 4th roots of -1?
14. T 18.0 What is (1 + i 3)8 ? Leave answer
in trigonometric (polar) form.
15. T 18.0 Express (-1 + i)10 in standard form.
16. MA 1.0 Name three representations for
point p:
5. T16.0 What is the polar form of the equation
3x - 4y = 12 ?
6. T 16.0 What is the polar equation for the
circle with the rectangular equation
x 2 + y 2 = 25 ?
p
π
0
7. T17.0 If z1 = 8(cos 45∞ + i sin 45∞) and
z2 = 4(cos 30∞ + i sin 30∞) ,
a) what is z1 ∑ z2 ?
b) what
z
is 1 ?
z2
4p
4p
8. T17.0 What is 2(cos
+ i sin ) in a + bi
3
3
form?
17. MA 1.0 A ship is heading north at 15 knots.
The current is moving northeast at 4 knots.
Draw a vector that represents the resulting
velocity of the ship.
9. T 17.0 What is the trigonometric (polar)
form of ( 3 - i) ?
18. MA 1.0 What is the rectangular form of the
equation 2 = r cos(q - 30∞) ?
10. T 17.0 What is the standard form (a + bi) of
3
5p
5p
the complex number (cos
+ i sin ) ?
2
3
3
19. MA 1.0 Rewrite the following polar
equation in rectangular form: r = 2csc q
Precalculus
Q3
Benchmark
Review
09‐10
Garden
Grove
Unified
School
District
Precalculus
Q3
Benchmark
Review
09‐10
Scientific
Calculators
are
permitted
20. MA 1.0 Which of the following polar
coordinates describes (- 3,1) ?
A. (2, 150°)
C. (-2, 150°)
B. (2, 30°)
D. (-2, 30°)
21. MA 1.0 What are the rectangular
coordinates of the point with polar coordinates
Ê 11p ˆ
Á 3,
˜?
Ë
6 ¯
22. MA 2.0 How is -169 + -25 - -100
written in a + bi form?
23. MA 2.0 What is the square of
6(cos 45∞ + i sin 45∞) ? Leave in polar form.
28. LA 7.0 In the figure below, which of the
following statements is true?


a
b

c
  
  
A. a + b = c
B. c+ b = a
 
 
C. a + c = b
D. b = c - a
29. LA 7.0 In parallelogram ABCD, vector AD
is 5,1 and vector AC is 10,5 . What is vector
AB?
B
C
A
D
24. MA 2.0 Find the cube of
5(cos20∞ + i sin 20∞) and express in standard
form.
30. LA 7.0 a vector has an initial point P(1, 2)
and a terminal point T(4, 4).
A) Find the component form of PT
B) Find the magnitude of PT
5p
5p ˆ
Ê
25. MA 2.0 What is 4 2 Á cos
+ i sin ˜ in
Ë
4
4¯
a + bi form?
31. LA 12.0 What is the dot product of
3, 4,-2 and 1,-3,-5 ?
26. MA 2.0 What is the value of (-1 + i) 7 ?


27. LA 7.0 Vectors a andb are shown below.

What is the sum of a and b ?

a

b

a = 7, 3

b = 5,6
Precalculus
Q3
Benchmark
Review
09‐10
32. LA 12.0 Which pair of vectors is
perpendicular? Explain why.
A. 3,-2 and -2, 3
B. 3,-2 and 2,-3
C. 3,-2 and 2, 3
D. 3,-2 and -3,2
Garden
Grove
Unified
School
District
Precalculus
Q3
Benchmark
Review
09‐10
Scientific
Calculators
are
permitted
33. LA 12.0 Under what conditions is vector
a, b perpendicular to vector 3,-1 ?
A. 3,-1 ∑ b, a
B. a, b ∑ 3,-1
C. 3,-1 ∑ a, b
D. a, b ∑ -1, 3
=0
=0
= -1
= -1
34. LA 12.0 The dot product of two vectors
produces:
A)
B)
C)
D)
a vector
A scalar
the magnitude of the vector
A direction angle
Precalculus
Q3
Benchmark
Review
09‐10
Garden
Grove
Unified
School
District
Precalculus
Q3
Benchmark
Review
09‐10
Scientific
Calculators
are
permitted
Answer Key
1. ( 61,50.2∞)
17.
2. (-3 3, 3)
Resultant vector
3. d
15
4. r = 6sin q
5. r =
12
3cosq - 4 sin q
4
6. r = 5
7. a) 32(cos 75∞ + i sin 75∞)
b) 2(cos15∞ + i sin15∞)
8. (-1,-i 3)
9. 2(cos
11p
11p
+ i sin
)
6
6
3 3 3
10. ( i)
4
4
11.
È Ê p 2pk ˆ
Ê p 2pk ˆ ˘
z = 3 1 ÍcosÁ +
˜ + i sin Á +
˜ when k = 0,1,2
Ë
¯
Ë6
6
3
3 ¯ ˙˚
Î
18. 4 =
3x + y
19. y = 2
20. A
Ê 3 3 3ˆ
21. Á
,- ˜
2¯
Ë 2
22. 8i
23. 36(cos90∞ + i sin 90∞)
125 125 3
24. (
+
i)
2
2
12.
2(cos45∞ + i sin 45∞), 2(cos165∞ + i sin165∞), 2(cos285∞ + i sin285∞)
25. -4 – 4i
13. (cos 45°+ i sin 45°), (cos 135°+ i sin 135°),
(cos 225°+ i sin 225°), (cos 315°+ i sin 315°)
26. -8 - 8i
14. 256(cos 120° + isin 120°)
15. -32i
16. Ex: (7,
5p
7p
p
), (7,- ), (-7,- )
6
6
6
Precalculus
Q3
Benchmark
Review
09‐10
27. 12,9
28. B
29. 5, 4
30.
31.
32.
33.
34.
A) (3, 2) B)
1
C
B
B
13